Abstract
Geodesic motion is completely integrable in the fields of isolated stationary black holes, but it may become chaotic if there exists some additional source in the space-time. The aim of the talk is to review previous results, in which the dynamics of such a system has been investigated by restricting to the static and axisymmetric case, and to outline future plans in which the research will be extended to the stationary case in order to study how the rotational dragging affects the chaoticity of the dynamics.